Details

Time bar (total: 6.6s)

analyze31.0ms (0.5%)

Algorithm
search
Search
TrueOtherFalseIter
0%37.5%62.5%0
0%37.5%62.5%1
0%18.7%81.3%2
0%9.4%90.6%3
0%9.4%90.6%4
0%7%93%5
1.2%4.7%94.1%6
1.2%3.5%95.3%7
1.8%2.6%95.6%8
2%1.9%96%9
2.4%1.3%96.3%10
2.6%1%96.5%11
2.7%0.7%96.6%12
2.8%0.5%96.7%13
2.9%0.3%96.7%14
Compiler

Compiled 26 to 15 computations (42.3% saved)

sample862.0ms (13%)

Results
762.0ms8256×body128valid
33.0ms352×body128invalid
Compiler

Compiled 67 to 38 computations (43.3% saved)

simplify88.0ms (1.3%)

Algorithm
egg-herbie
Rules
704×fma-def_binary64
643×fma-neg_binary64
603×associate-/r*_binary64
566×associate-*l*_binary64
362×distribute-rgt-in_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0920
12617
26915
319415
446415
5152115
6478115
7516015

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
16.2b
Counts
3 → 1
Alt Table
StatusErrorProgram
16.2b
(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
Compiler

Compiled 49 to 29 computations (40.8% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
0.0b
(fma.f64 b (/.f64 b (*.f64 a a)) -1)
16.3b
(/.f64 b (*.f64 a a))

series62.0ms (0.9%)

Counts
3 → 72
Calls

3 calls:

27.0ms
(/.f64 b (*.f64 a a))
23.0ms
(fma.f64 b (/.f64 b (*.f64 a a)) -1)
12.0ms
(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

rewrite7.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
sqrt-prod_binary64
*-un-lft-identity_binary64
Counts
3 → 54
Calls

3 calls:

3.0ms
(/.f64 b (*.f64 a a))
1.0ms
(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
0.0ms
(fma.f64 b (/.f64 b (*.f64 a a)) -1)

simplify103.0ms (1.6%)

Algorithm
egg-herbie
Rules
661×associate-/l*_binary64
603×fma-def_binary64
491×associate-*l*_binary64
486×associate-/l/_binary64
431×associate-/r*_binary64
Counts
126 → 70
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0901587
11431492
22931492
38661490
445081490
550631490

prune200.0ms (3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New67370
Fresh000
Picked101
Done000
Total68371
Error
0.0b
Counts
71 → 3
Alt Table
StatusErrorProgram
0.0b
(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 1 (/.f64 a (/.f64 b a))) -1)))
16.2b
(sqrt.f64 (fabs.f64 (cbrt.f64 (pow.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1) 3))))
16.2b
(sqrt.f64 (fabs.f64 (log1p.f64 (expm1.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))))
Compiler

Compiled 1165 to 577 computations (50.5% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 1 (/.f64 a (/.f64 b a))) -1)))
0.0b
(fma.f64 b (/.f64 1 (/.f64 a (/.f64 b a))) -1)
0.3b
(/.f64 1 (/.f64 a (/.f64 b a)))
0.3b
(/.f64 a (/.f64 b a))

series138.0ms (2.1%)

Counts
4 → 96
Calls

4 calls:

52.0ms
(fma.f64 b (/.f64 1 (/.f64 a (/.f64 b a))) -1)
45.0ms
(/.f64 1 (/.f64 a (/.f64 b a)))
21.0ms
(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 1 (/.f64 a (/.f64 b a))) -1)))
20.0ms
(/.f64 a (/.f64 b a))

rewrite90.0ms (1.4%)

Algorithm
rewrite-expression-head
Rules
471×times-frac_binary64
237×add-sqr-sqrt_binary64
233×*-un-lft-identity_binary64
233×add-cube-cbrt_binary64
57×associate-/r*_binary64
Counts
4 → 309
Calls

4 calls:

18.0ms
(/.f64 1 (/.f64 a (/.f64 b a)))
10.0ms
(/.f64 a (/.f64 b a))
1.0ms
(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 1 (/.f64 a (/.f64 b a))) -1)))
1.0ms
(fma.f64 b (/.f64 1 (/.f64 a (/.f64 b a))) -1)

simplify586.0ms (8.9%)

Algorithm
egg-herbie
Rules
486×fma-neg_binary64
352×fma-def_binary64
313×*-commutative_binary64
297×associate-/r/_binary64
260×unswap-sqr_binary64
Counts
405 → 459
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02877610
15326535
215436124
318746072
427545918
546375918
649465918

prune847.0ms (12.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New4572459
Fresh112
Picked101
Done000
Total4593462
Error
0.0b
Counts
462 → 3
Alt Table
StatusErrorProgram
16.2b
(sqrt.f64 (fabs.f64 (cbrt.f64 (pow.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1) 3))))
0.0b
(sqrt.f64 (fabs.f64 (+.f64 (*.f64 b (/.f64 1 (/.f64 a (/.f64 b a)))) -1)))
16.2b
(log.f64 (exp.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))))
Compiler

Compiled 10128 to 4610 computations (54.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 b (/.f64 1 (/.f64 a (/.f64 b a)))) -1)
0.2b
(*.f64 b (/.f64 1 (/.f64 a (/.f64 b a))))
0.3b
(/.f64 1 (/.f64 a (/.f64 b a)))
0.3b
(/.f64 a (/.f64 b a))

series483.0ms (7.3%)

Counts
2 → 48
Calls

2 calls:

444.0ms
(*.f64 b (/.f64 1 (/.f64 a (/.f64 b a))))
39.0ms
(+.f64 (*.f64 b (/.f64 1 (/.f64 a (/.f64 b a)))) -1)

rewrite118.0ms (1.8%)

Algorithm
rewrite-expression-head
Rules
342×times-frac_binary64
176×add-sqr-sqrt_binary64
156×*-un-lft-identity_binary64
153×add-cube-cbrt_binary64
137×associate-*r*_binary64
Counts
2 → 188
Calls

2 calls:

58.0ms
(*.f64 b (/.f64 1 (/.f64 a (/.f64 b a))))
24.0ms
(+.f64 (*.f64 b (/.f64 1 (/.f64 a (/.f64 b a)))) -1)

simplify317.0ms (4.8%)

Algorithm
egg-herbie
Rules
762×fma-neg_binary64
417×*-commutative_binary64
256×unswap-sqr_binary64
228×associate-/r/_binary64
191×cancel-sign-sub-inv_binary64
Counts
236 → 335
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02383345
15483148
219612885
328192817
448342817
552692817

prune1.1s (17.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New7361737
Fresh112
Picked011
Done000
Total7373740
Error
0.0b
Counts
740 → 3
Alt Table
StatusErrorProgram
16.2b
(sqrt.f64 (fabs.f64 (cbrt.f64 (pow.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1) 3))))
0.0b
(sqrt.f64 (fabs.f64 (+.f64 (*.f64 b (/.f64 1 (/.f64 a (/.f64 b a)))) -1)))
0.0b
(sqrt.f64 (fabs.f64 (log1p.f64 (expm1.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))
Compiler

Compiled 17680 to 8178 computations (53.7% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (fabs.f64 (log1p.f64 (expm1.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))
0.0b
(fma.f64 b (/.f64 (/.f64 b a) a) -1)
0.0b
(log1p.f64 (expm1.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))
0.3b
(/.f64 (/.f64 b a) a)

series272.0ms (4.1%)

Counts
4 → 96
Calls

4 calls:

145.0ms
(/.f64 (/.f64 b a) a)
53.0ms
(fma.f64 b (/.f64 (/.f64 b a) a) -1)
42.0ms
(log1p.f64 (expm1.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))
31.0ms
(sqrt.f64 (fabs.f64 (log1p.f64 (expm1.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))

rewrite32.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
75×times-frac_binary64
52×add-sqr-sqrt_binary64
48×*-un-lft-identity_binary64
48×add-cube-cbrt_binary64
13×associate-/l*_binary64
Counts
4 → 114
Calls

4 calls:

10.0ms
(/.f64 (/.f64 b a) a)
3.0ms
(sqrt.f64 (fabs.f64 (log1p.f64 (expm1.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))
1.0ms
(fma.f64 b (/.f64 (/.f64 b a) a) -1)
1.0ms
(log1p.f64 (expm1.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))

simplify269.0ms (4.1%)

Algorithm
egg-herbie
Rules
599×fma-def_binary64
423×unswap-sqr_binary64
394×fma-neg_binary64
337×associate-/l/_binary64
324×times-frac_binary64
Counts
210 → 175
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01953073
13502841
26532769
316952745
426362725
546452725
649582725

prune258.0ms (3.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1750175
Fresh011
Picked011
Done011
Total1753178
Error
0.0b
Counts
178 → 3
Alt Table
StatusErrorProgram
16.2b
(sqrt.f64 (fabs.f64 (cbrt.f64 (pow.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1) 3))))
0.0b
(sqrt.f64 (fabs.f64 (+.f64 (*.f64 b (/.f64 1 (/.f64 a (/.f64 b a)))) -1)))
0.0b
(sqrt.f64 (fabs.f64 (log1p.f64 (expm1.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))
Compiler

Compiled 3430 to 1688 computations (50.8% saved)

regimes526.0ms (8%)

Accuracy

Total 0.0b remaining (46.5%)

Threshold costs 0.0b (46.5%)

Counts
42 → 1
Compiler

Compiled 4771 to 3286 computations (31.1% saved)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01116
11216
21216

end120.0ms (1.8%)

Compiler

Compiled 68 to 52 computations (23.5% saved)

Profiling

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